Finite Math Examples

\begin{array}{c} x & y \\ - 1 & - 3.49 \\ 0 & 1.2 \\ 1 & 0.88 \\ 2 & - 4.5 \\ 3 & - 12.9 \end{array}

$\begin{array}{c} x & y \\ - 1 & - 3.49 \\ 0 & 1.2 \\ 1 & 0.88 \\ 2 & - 4.5 \\ 3 & - 12.9 \end{array}$

Step 1

The linear correlation coefficient measures the relationship between the paired values in a sample.

r = \frac{n (\sum_{}^{} x y) - \sum_{}^{} x \sum_{}^{} y}{\sqrt{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}} \cdot \sqrt{n (\sum_{}^{} y^{2}) - {(\sum_{}^{} y)}^{2}}}

$r = \frac{n (\sum_{}^{} x y) - \sum_{}^{} x \sum_{}^{} y}{\sqrt{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}} \cdot \sqrt{n (\sum_{}^{} y^{2}) - {(\sum_{}^{} y)}^{2}}}$

Step 2

Sum up the

x

$x$ values.

\sum_{}^{} x = - 1 + 0 + 1 + 2 + 3

$\sum_{}^{} x = - 1 + 0 + 1 + 2 + 3$

Step 3

Simplify the expression.

\sum_{}^{} x = 5

$\sum_{}^{} x = 5$

Step 4

Sum up the

y

$y$ values.

\sum_{}^{} y = - 3.49 + 1.2 + 0.88 - 4.5 - 12.9

$\sum_{}^{} y = - 3.49 + 1.2 + 0.88 - 4.5 - 12.9$

Step 5

Simplify the expression.

\sum_{}^{} y = - 18.81

$\sum_{}^{} y = - 18.81$

Step 6

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum_{}^{} x y = - 1 \cdot - 3.49 + 0 \cdot 1.2 + 1 \cdot 0.88 + 2 \cdot - 4.5 + 3 \cdot - 12.9

$\sum_{}^{} x y = - 1 \cdot - 3.49 + 0 \cdot 1.2 + 1 \cdot 0.88 + 2 \cdot - 4.5 + 3 \cdot - 12.9$

Step 7

Simplify the expression.

\sum_{}^{} x y = - 43.329998

$\sum_{}^{} x y = - 43.329998$

Step 8

Sum up the values of

x^{2}

$x^{2}$ .

\sum_{}^{} x^{2} = {(- 1)}^{2} + {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}

$\sum_{}^{} x^{2} = {(- 1)}^{2} + {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}$

Step 9

Simplify the expression.

\sum_{}^{} x^{2} = 15

$\sum_{}^{} x^{2} = 15$

Step 10

Sum up the values of

y^{2}

$y^{2}$ .

\sum_{}^{} y^{2} = {(- 3.49)}^{2} + {(1.2)}^{2} + {(0.88)}^{2} + {(- 4.5)}^{2} + {(- 12.9)}^{2}

$\sum_{}^{} y^{2} = {(- 3.49)}^{2} + {(1.2)}^{2} + {(0.88)}^{2} + {(- 4.5)}^{2} + {(- 12.9)}^{2}$

Step 11

Simplify the expression.

\sum_{}^{} y^{2} = 201.05449033

$\sum_{}^{} y^{2} = 201.05449033$

Step 12

Fill in the computed values.

r = \frac{5 (- 43.329998) - 5 \cdot - 18.81}{\sqrt{5 (15) - {(5)}^{2}} \cdot \sqrt{5 (201.05449) - {(- 18.81)}^{2}}}

$r = \frac{5 (- 43.329998) - 5 \cdot - 18.81}{\sqrt{5 (15) - {(5)}^{2}} \cdot \sqrt{5 (201.05449) - {(- 18.81)}^{2}}}$

Step 13

Simplify the expression.

r = - 0.67930184

$r = - 0.67930184$